# Syllabus

## Table of contents

## Overview

In this course, our aim is to explain this beautiful and useful part of mathematics. We’ ll start with solving linear equations $A\mathbf{x}=\mathbf{b}$. The vector of $A\mathbf{x}$ is a linear combination of the columns of $A$. By solving the equations, We’ll introduce the four fundamental subspaces for the matrix $A$. Then we’ll explain the fundamental theorem of linear algebra. Also we’ll show some applications.

By the end of the course, students will learn:

- The row and column picture of $A\mathbf{x}=\mathbf{b}$, and hence the elimination in the beautiful form $A=LU$.
- The concept of subspace and the four fundamental subspaces for the matrix $A$.
- Determinants.
- Eigenvalues and eigenvectors.
- Linear transformations.
- Singular value decomposition.(SVD)
- Applications of linear algebra.

## Policies

### Cheating

You are encouraged to collaborate with your classmates or utilize online resources for any homework. Actually, you can also ask for the instructor. **However, directly copying and pasting code or answers is prohibited.** If I ask you how you proved or why your answers are correct and you do not know, it will be evident that you have copied it. Don’t take the risk.

### Homework

The **HW** will be released once a week.

**Please note that late submissions will incur a 25% penalty.**

### Final Exam

This course will have only one exam, the final exam. The more information will be decided later.

### Grades

Students’ grades**Grade** will be determined by the following two components:

- Homework
**HW**, - Final Exam
**Exam**,

- The final grade will be calculated using the following equation:
**Grade**= 40%***HW**+ 60%***Exam**## Resources

This course website, Linear Algebra, will be your one-stop resource for the syllabus, schedule and homework links.

**Reference**

Here’re some recommended books：

- [1] Gilbert Strang.
*Introduction to Linear Algebra*. - [2] 同济大学数学科学学院。
*工程数学线性代数(第7版)*

Some online resources:

- [1] MIT 18.06
- [2] MIT线性代数公开课B站搬运